1. Field of the Invention
The present invention relates to a method of preparing a fluid-structure interactive numerical model for preparing a numerical model related to a fluid and a numerical model related to a structure when an actual structure as a living organism performs a prescribed motion in the fluid, as well as to a method of manufacturing a fluttering robot using the same.
2. Description of the Background Art
Conventionally, attempts have been made to prepare a numerical model of the manner of fluttering flight that mimics the flight of an insect as an example of a structure of a living organism, with the manner of flight given as numerical expression, by a computer. Further, a simulator or a game of fluttering flight has been known that utilizes the thus prepared numerical model, in which the manner of fluttering flight mimicking an insect is displayed on a display.
In this field of art, it is very useful to analyze a prescribed motion of a structure as a living organism in a fluid, that is, fluttering motion of an actual insect in the air, to know the mechanism of fluttering flight and to use the knowledge for controlling a fluttering robot that flies fluttering. The reason for this is that there is an almost infinite combinations of the manner of fluttering and the wing shapes of insects, and hence a formidable time is necessary to optimize the manner of fluttering or the wing shape of the insect, to meet a requested specification of the fluttering flight, and hence such an approach is impractical. In the course of evolution, insects have their manner of fluttering or wing shapes optimized. Therefore, as can be seen from the fact that bird wings are considered in designing glider wings, the method of obtaining basic principle of fluttering flight from insects is very efficient as compared with other methods.
Further, it is very useful in the industry to prepare a new numerical model by modifying the numerical model related to the air and the numerical model related to the wing structure of an insect obtained from the insect so as to feed back the influence of the modification for better suited wing structure and analysis of the manner of fluttering.
Therefore, in preparing a numerical model of the manner of fluttering, a method has been considered in which wing motion is extracted from images of fluttering flight of an insect picked-up by a high speed camera and obtain data of the extracted wing motion successively by image processing, for example.
In order to analyze air behavior associated with fluttering, a method has been used in which an insect flies in a wind tunnel in which a trace such as a smoke flows and the behavior of the trace is monitored.
Recently, an experiment has been conducted in which a scaled model of a wing is moved in a fluid having high viscosity such as mineral oil, so as to prepare an environment in which the Reynolds number of the fluid is made equal to the Reynolds number of the air, though the manner of fluttering is far moderate than the actual manner of fluttering of an insect, so as to facilitate measurement of velocity when the insect flies fluttering at high speed.
In the above described method, however, it is impossible to simultaneously obtain the behavior of the air as the fluid and the behavior of the insect as a structure of a living organism. Therefore, it has been impossible to prepare a numerical model that involves interaction between the air and the wing of the insect, that is, to prepare a fluid-structure interactive numerical model.
In the following, conventional methods of preparing numerical models will be specifically described.
(1) Method of Getting Numerical Expression of Wing Deformation Using High Speed Camera
According to A. Azuma, “The Biokinetics of flying and swimming” Springer-Verlag, Tokyo, 1992, a high speed camera is used, and positions of a line marker marked on a wing of an insect are captured to obtain attitude of the wing. Given the image processing capability of presently used computers, it is possible to obtain numerical expression, including change in shape, the manner of fluttering of a wing, by observing featured portion of the pattern of the entire wing, using video images obtained by the high speed image-pickup.
Though it is possible by this method to grasp the wing behavior, it is not at all possible to grasp fluid behavior. Therefore, when an image is to be displayed on a computer using a numerical model related to the fluttering flight of an insect, for example, it is possible to express fluttering motion, where influence of air flow made by the wing on other structures cannot be calculated.
(2) Fluid Flux Observation Using Trace
A method in which a trace such as smoke is caused to flow in a wind tunnel to visualize the fluid flux of the trace has been long used for analyzing not only the fluttering flight of an insect but general behavior of a fluid.
What is obtained by this method, however, is the shape of the fluid flux of the trace and not the velocity of the flowing trace. Therefore, it has been unsuccessful to obtain numerical model of the fluid behavior.
As a similar method using a trace, a method has been recently applied to measure velocity in a pump, in which colored particles having approximately the same density as the fluid in the pump are caused to flow in the fluid, the manner of movement of the particles is detected by image processing, and the manner of movement is time-differentiated, to measure the velocity.
It is noted, however, that only extremely small particles can float and not fall down, over a long period of time in a fluid having very small density such as air. Therefore, considering the capability of identification by a camera, it is impossible to use this method when the fluid is air.
Consider analysis of fluttering of a dragon fly for one period. The fluttering period of a dragon fly is about 30 Hz, and the velocity caused by the fluttering is about 10 m/sec. Therefore, one particle of the smoke moves by the distance of 30 cm in this period. Therefore, in order to measure velocity of one period of fluttering of a dragon fly, that is, in order to measure the manner of movement of a certain trace, it is necessary to pick-up an image of at least an area of 30 cm×30 cm.
When the area of 30 cm×30 cm is picked-up by a CCD camera having 1000 pixels×1000 pixels, it follows that an area of 300 μm×300 μm is picked-up by one pixel. The diameter of a particle that can float over a long period of time in the air, such as a pollen, is about 3 μm. The seeming area of the particle 3 μm in diameter is only 1/10000 of the area picked-up by 1 pixel. Assuming that the light reflectance is the same, the trace floating in the air has the luminance of 1/10000 of the luminance of an ordinary object having such an area that can be captured by a plurality of pixels.
The inventors of the present invention conducted an experiment. An object having sufficiently large area is picked-up by a high speed camera under the illumination of 40000 lux. Even in this experiment, only 1024 frames at most could be picked-up in 1 second, using a microlens of 105 mmf 2.8 and a CCD camera comparable to ISO100. When an object moving with to period of about 30 Hz is to be captured with high accuracy as video images, the number of frames as high as 1024 is still insufficient. In order to capture to movement of a particle of 3 μm as video images, it follows that the product of CCD camera sensitivity and the luminance of illumination must be multiplied 10000 times. Therefore, such a method is considered impractical.
(3) Measurement of Fluid Using Scaled Model
M. Dickinson et al. (SCIENCE 1999 Vol. 284 pp. 1954-1960 “Wing Rotation and the Aerodynamic Basis of Insect Flight”) noted that fluid having the same Reynolds number behave equivalently, and found a method in which a large scaled wing model is moved at a velocity of at most several Hz in a mineral oil having high viscosity, whereby movement of particles mixed in a fluid that is equivalent to the fluttering of a fly and corresponds to the particles described in item (2) above is detected by image processing, enabling measurement of the movement.
It is truth that when the Reynolds number is the same, fluid of different types behave in the same manner. The behavior of particle structures moving in fluid of different types but having the same Reynolds number, however, differ considerably. Therefore, by this method, it is impossible to correctly grasp deformation of particle structure moving in the fluid.
For example, the relation of velocity F=s×f always holds where s represents scale and f represents velocity of the air in which an actual fly moves fluttering. As to the deformation D of actual fly wing, wing deformation D=s×d holds for some deformation d, while it does not hold for other deformation d.
As described above, it has been unsuccessful through conventional methods to prepare an interactive numerical model between fluid and structure. For example, it has been impossible to properly represent a movement of a petal when a butterfly rests on a flower.
By any of the above described methods, it has been impossible to calculate torque for driving the wing, for example, for a fluttering robot that mimics motion of a wing of an insect, since in methods (1) and (2), actual measurement of physical parameters is impossible and in method (3), force used for deformation of the wing is not considered as the wing deformation is different from the actual structure. Therefore, it has been difficult to obtain numerical model of a driving force for driving the wing, which is most important in forming a control mechanism controlling the fluttering flight.
In short, by the numerical models prepared in accordance with the prior art, it has been difficult to obtain numerical expression of motion of a structure, which is a living organism, in a fluid, including fluid-structure interaction.
Further, when a robot mimicking the structure as a living organism is to be manufactured, it has been necessary to design the driving force, allowing for a margin of the driving force, as it has been difficult to calculate the numerical model of driving force for driving the structure as a living organism.
By any of the conventional methods, it is impossible to prepare a numerical model of the manner of fluttering flight of the robot mentioned above. Attempts have been made to actually fabricate the fluttering flight robot as described above, to drive the fluttering robot in various different manners of driving, and to prepare a numerical model of the manner of fluttering drive through trial and error. When the manner of fluttering drive that brings about the manner of motion such as a turn or a change in attitude is to be studied, it is first of all necessary that conditions to lift the fluttering robot are satisfied. Therefore, such a study can be made only under very limited conditions. Therefore, either by the method using a numerical model or by the method through experiment, it has been difficult to efficiently find the manner of fluttering drive of a fluttering robot.